The synchronization of FitzHugh–Nagumo neuron network coupled by gap junction

Abstract

It is well known that the strong coupling can synchronize a network of nonlinear oscillators. Synchronization provides the basis of the remarkable computational performance of the brain. In this paper the FitzHugh–Nagumo neuron network is constructed. The dependence of the synchronization on the coupling strength, the noise intensity and the size of the neuron network has been discussed. The results indicate that the coupling among neurons works to improve the synchronization, and noise increases the neuron random dynamics and the local fluctuations; the larger the size of network, the worse the synchronization. The dependence of the synchronization on the strength of the electric synapse coupling and chemical synapse coupling has also been discussed, which proves that electric synapse coupling can enhance the synchronization of the neuron network largely.

Feedback Synchronization of FHN Cellular Neural Networks

“…In this work, we consider a CNN model as the discrete replacement of the biological neural networks described by the partial diffusive FitzHugh-Nagumo equations with different coupling patterns [11,19,20,23,24],…”

“…Synchronization for biological neural networks has been studied by several mathematical models and methods. This topic has been studied for the diffusive FitzHuigh-Nagumo networks of neurons coupled by clamped gap junctions [1,2,3,13,24], the mean field couplings of Hodgkin-Huxley and FitzHuigh-Nagumo neuron networks [10,17], and the chaotic neural networks and stochastic neural networks [10,18].…”

Dynamics and Synchronization of Boundary Coupled FitzHugh-Nagumo Neural Networks

“…Synchronization for biological neural networks has been studied by using several mathematical models and methods. Most published results are for the FitzHuigh-Nagumo networks of neurons coupled by gap junctions or called space-clamped coupling [5,17,37,39] featuring the linear coupling C j( =i) a ij (x j (t) − x i (t)) in the membrane potential equation for the i-th neuron. The mean field models of Hodgkin-Huxley and FitzHuigh-Nagumo neuron networks may or may not with noise were studied in [3,8,27,34] replacing the above sum of couplings by its average.…”

Feedback synchronization of FHN cellular neural networks

“…In this work, we consider a CNN model as the discrete replacement of the biological neural networks described by the partially diffusive FitzHugh-Nagumo equations with different coupling patterns [11,19,20,23,24],…”

“…Synchronization for biological neural networks has been studied by using several mathematical models and methods. This topic has been studied for the diffusive FitzHuigh-Nagumo networks of neurons coupled by clamped gap junctions [1,2,3,13,24], the mean field couplings of Hodgkin-Huxley and FitzHuigh-Nagumo neuron networks [10,17], the chaotic neural networks and stochastic neural networks [10,18].…”